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Background: Ensuring fair comparisons of cancer survival statistics across population groups requires careful consideration of differential competing mortality due to other causes, and adjusting for imbalances over groups in other prognostic covariates (e.g. age). This has typically been achieved using comparisons of age-standardised net survival, with age standardisation addressing covariate imbalance, and the net estimates removing differences in competing mortality from other causes. However, these estimates lack ease of interpretability. In this paper, we motivate an alternative non-parametric approach that uses a common rate of other cause mortality across groups to give reference-adjusted estimates of the all-cause and cause-specific crude probability of death in contrast to solely reporting net survival estimates.Methods: We develop the methodology for a non-parametric equivalent of standardised and reference adjusted crude probabilities of death, building on the estimation of non-parametric crude probabilities of death. We illustrate the approach using regional comparisons of survival following a diagnosis of rectal cancer for men in England. We standardise to the covariate distribution and other cause mortality of England as a whole to offer comparability, but with close approximation to the observed all-cause region-specific mortality.Results: The approach gives comparable estimates to observed crude probabilities of death, but allows direct comparison across population groups with different covariate profiles and competing mortality patterns. In our illustrative example, we show that regional variations in survival following a diagnosis of rectal cancer persist even after accounting for the variation in deprivation, age at diagnosis and other cause mortality.Conclusions: The methodological approach of using standardised and reference adjusted metrics offers an appealing approach for future cancer survival comparison studies and routinely published cancer statistics. Our non-parametric estimation approach through the use of weighting offers the ability to estimate comparable survival estimates without the need for statistical modelling. [ABSTRACT FROM AUTHOR]

Background: Competing risks are a common occurrence in survival analysis. They arise when a patient is at risk of more than one mutually exclusive event, such as death from different causes, and the occurrence of one of these may prevent any other event from ever happening. Methods: There are two main approaches to modelling competing risks: the first is to model the cause-specific hazards and transform these to the cumulative incidence function; the second is to model directly on a transformation of the cumulative incidence function. We focus on the first approach in this paper. This paper advocates the use of the flexible parametric survival model in this competing risk framework. Results: An illustrative example on the survival of breast cancer patients has shown that the flexible parametric proportional hazards model has almost perfect agreement with the Cox proportional hazards model. However, the large epidemiological data set used here shows clear evidence of non-proportional hazards. The flexible parametric model is able to adequately account for these through the incorporation of time-dependent effects. Conclusion: A key advantage of using this approach is that smooth estimates of both the cause-specific hazard rates and the cumulative incidence functions can be obtained. It is also relatively easy to incorporate time-dependent effects which are commonly seen in epidemiological studies. [ABSTRACT FROM AUTHOR]

Background: Under competing risks, the commonly used sub-distribution hazard ratio (SHR) is not easy to interpret clinically and is valid only under the proportional sub-distribution hazard (SDH) assumption. This paper introduces an alternative statistical measure: the restricted mean time lost (RMTL).Methods: First, the definition and estimation methods of the measures are introduced. Second, based on the differences in RMTLs, a basic difference test (Diff) and a supremum difference test (sDiff) are constructed. Then, the corresponding sample size estimation method is proposed. The statistical properties of the methods and the estimated sample size are evaluated using Monte Carlo simulations, and these methods are also applied to two real examples.Results: The simulation results show that sDiff performs well and has relatively high test efficiency in most situations. Regarding sample size calculation, sDiff exhibits good performance in various situations. The methods are illustrated using two examples.Conclusions: RMTL can meaningfully summarize treatment effects for clinical decision making, which can then be reported with the SDH ratio for competing risks data. The proposed sDiff test and the two calculated sample size formulas have wide applicability and can be considered in real data analysis and trial design. [ABSTRACT FROM AUTHOR]

Background: Patients infected with the Human Immunodeficiency Virus (HIV) are susceptible to many diseases. In these patients, the occurrence of one disease alters the chance of contracting another. Under such circumstances, methods for competing risks are required. Recently, competing risks analyses in the scope of flexible parametric models have risen to address this requirement. These lesser-known analyses have considerable advantages over conventional methods.Methods: Using data from Multi Centre AIDS Cohort Study (MACS), this paper reviews and applies methods of competing risks flexible parametric models to analyze the risk of the first disease (AIDS or non-AIDS) among HIV-infected patients. We compared two alternative subdistribution hazard flexible parametric models (SDHFPM1 and SDHFPM2) with the Fine & Gray model. To make a complete inference, we performed cause-specific hazard flexible parametric models for each event separately as well.Results: Both SDHFPM1 and SDHFPM2 provided consistent results regarding the magnitude of coefficients and risk estimations compared with estimations obtained from the Fine & Gray model, However, competing risks flexible parametric models provided more efficient and smoother estimations for the baseline risks of the first disease. We found that age at HIV diagnosis indirectly affected the risk of AIDS as the first event by increasing the number of patients who experience a non-AIDS disease prior to AIDS among > 40 years. Other significant covariates had direct effects on the risks of AIDS and non-AIDS.Discussion: The choice of an appropriate model depends on the research goals and computational challenges. The SDHFPM1 models each event separately and requires calculating censoring weights which is time-consuming. In contrast, SDHFPM2 models all events simultaneously and is more appropriate for large datasets, however, when the focus is on one particular event SDHFPM1 is more preferable. [ABSTRACT FROM AUTHOR]

Background: To illustrate the 10-year risks of urinary adverse events (UAEs) among men diagnosed with prostate cancer and treated with different types of therapy, accounting for the competing risk of death.Methods: Prostate cancer is the second most common malignancy among adult males in the United States. Few studies have reported the long-term post-treatment risk of UAEs and those that have, have not appropriately accounted for competing deaths. This paper conducts an inverse probability of treatment (IPT) weighted competing risks analysis to estimate the effects of different prostate cancer treatments on the risk of UAE, using a matched-cohort of prostate cancer/non-cancer control patients from the Surveillance, Epidemiology and End Results (SEER) Medicare database.Results: Study dataset included men age 66 years or older that are 83% white and had a median follow-up time of 4.14 years. Patients that underwent combination radical prostatectomy and external beam radiotherapy experienced the highest risk of UAE (IPT-weighted competing risks: HR 3.65 with 95% CI (3.28, 4.07); 10-yr. cumulative incidence = 36.5%).Conclusions: Findings suggest that IPT-weighted competing risks analysis provides an accurate estimator of the cumulative incidence of UAE taking into account the competing deaths as well as measured confounding bias. [ABSTRACT FROM AUTHOR]

Background: In any single-arm trial on novel treatments, assessment of toxicity plays an important role as occurrence of adverse events (AEs) is relevant for application in clinical practice. In the presence of a non-fatal time-to-event(s) efficacy endpoint, the analysis should be broadened to consider AEs occurrence in time. The AEs analysis could be tackled with two approaches, depending on the clinical question of interest. Approach 1 focuses on the occurrence of AE as first event. Treatment ability to protect from the efficacy endpoint event(s) has an impact on the chance of observing AEs due to competing risks action. Approach 2 considers how treatment affects the occurrence of AEs in the potential framework where the efficacy endpoint event(s) could not occur. Methods: In the first part of the work we review the strategy of analysis for these two approaches. We identify theoretical quantities and estimators consistent with the following features: (a) estimators should address for the presence of right censoring; (b) theoretical quantities and estimators should be functions of time. In the second part of the work we propose the use of alternative methods (regression models, stratified Kaplan-Meier curves, inverse probability of censoring weighting) to relax the assumption of independence between the potential times to AE and to event(s) in the efficacy endpoint for addressing Approach 2. Results: We show through simulations that the proposed methods overcome the bias due to the dependence between the two potential times and related to the use of standard estimators. Conclusions: We demonstrated through simulations that one can handle patients selection in the risk sets due to the competing event, and thus obtain conditional independence between the two potential times, adjusting for all the observed covariates that induce dependence. [ABSTRACT FROM AUTHOR]

Background: Real-world observational data are an important source of evidence on the treatment effectiveness for patients hospitalized with coronavirus disease 2019 (COVID-19). However, observational studies evaluating treatment effectiveness based on longitudinal data are often prone to methodological biases such as immortal time bias, confounding bias, and competing risks. Methods: For exemplary target trial emulation, we used a cohort of patients hospitalized with COVID-19 (n = 501) in a single centre. We described the methodology for evaluating the effectiveness of a single-dose treatment, emulated a trial using real-world data, and drafted a hypothetical study protocol describing the main components. To avoid immortal time and time-fixed confounding biases, we applied the clone-censor-weight technique. We set a 5-day grace period as a period of time when treatment could be initiated. We used the inverse probability of censoring weights to account for the selection bias introduced by artificial censoring. To estimate the treatment effects, we took the multi-state model approach. We considered a multi-state model with five states. The primary endpoint was defined as clinical severity status, assessed by a 5-point ordinal scale on day 30. Differences between the treatment group and standard of care treatment group were calculated using a proportional odds model and shown as odds ratios. Additionally, the weighted cause-specific hazards and transition probabilities for each treatment arm were presented. Results: Our study demonstrates that trial emulation with a multi-state model analysis is a suitable approach to address observational data limitations, evaluate treatment effects on clinically heterogeneous in-hospital death and discharge alive endpoints, and consider the intermediate state of admission to ICU. The multi-state model analysis allows us to summarize results using stacked probability plots that make it easier to interpret results. Conclusions: Extending the emulated target trial approach to multi-state model analysis complements treatment effectiveness analysis by gaining information on competing events. Combining two methodologies offers an option to address immortal time bias, confounding bias, and competing risk events. This methodological approach can provide additional insight for decision-making, particularly when data from randomized controlled trials (RCTs) are unavailable. [ABSTRACT FROM AUTHOR]

Safety is an essential part of the evaluation of new medications and competing risks that occur in most clinical trials are a well identified challenge in the analysis of adverse events. Two statistical frameworks exist to consider competing risks: the cause-specific and the subdistribution framework. To date, the application of the cause-specific framework is the standard practice in safety analyses. Here we analyze how the safety analysis results of new medications would be affected if instead of the cause-specific the subdistribution framework was chosen. We conducted a simulation study with 600 participants, equally allocated to verum and control groups and a 30 months follow-up period. Simulated trials were analyzed for safety in a competing risk (death) setting using both the cause-specific and subdistribution frameworks. Results show that comparing safety profiles in a subdistribution setting is always more pessimistic than in a cause-specific setting. For the group with the longest survival and a safety advantage in a cause-specific setting, the advantage either disappeared or a disadvantage was found in the subdistribution analysis setting. These observations are not contradictory but show different perspectives. To evaluate the safety of a new medication over its comparator, one needs to understand the origin of both the risks and the benefits associated with each therapy. These requirements are best met with a cause-specific framework. The subdistribution framework seems better suited for clinical prediction, and therefore more relevant for providers or payers, for example. [ABSTRACT FROM AUTHOR]

Background: In many clinical trials the study interest lies in the comparison of a treatment to a control group regarding a time to event endpoint like time to myocardial infarction, time to relapse, or time to a specific cause of death. Thereby, an event can occur before the primary event of interest that alters the risk for or prohibits observing the latter, i.e. a competing event. Furthermore, multi-center studies are often conducted. Hence, a cluster structure might be observed. However, commonly only the aspect of competing events or the aspect of the cluster structure is modelled within primary analysis, although both are given within the study design. Methods to adequately analyze data in such a design were recently described but were not systematically compared yet. Methods: Within this work we provide a systematic comparison of four approaches for the analysis of competing events where a cluster structure is present based on a real life data set and a simulation study. The considered methods are the commonly applied cause-specific Cox proportional hazards model with a frailty, the Fine and Gray model for considering competing risks, and extensions of the latter model by Katsahian et al. and Zhou et al. Results: Based on our simulation results, the model by Katsahian et al. showed the best performance in bias, square root of mean squared error, and power in nearly all scenarios. In contrast to the other three models this approach allows both unbiased effect estimation and prognosis. Conclusion: The provided comparison and simulations help to guide applied researchers to choose an adequate method for the analysis of competing events where a cluster structure is present. Based on our simulation results the approach by Katsahian et al. can be recommended. [ABSTRACT FROM AUTHOR]

Background: The analysis of time-to-event data can be complicated by competing risks, which are events that alter the probability of, or completely preclude the occurrence of an event of interest. This is distinct from censoring, which merely prevents us from observing the time at which the event of interest occurs. However, the censoring distribution plays a vital role in the proportional subdistribution hazards model, a commonly used method for regression analysis of time-to-event data in the presence of competing risks.Methods: We present the equations that underlie the proportional subdistribution hazards model to highlight the way in which the censoring distribution is included in its estimation via risk set weights. By simulating competing risk data under a proportional subdistribution hazards model with different patterns of censoring, we examine the properties of the estimates from such a model when the censoring distribution is misspecified. We use an example from stem cell transplantation in multiple myeloma to illustrate the issue in real data.Results: Models that correctly specified the censoring distribution performed better than those that did not, giving lower bias and variance in the estimate of the subdistribution hazard ratio. In particular, when the covariate of interest does not affect the censoring distribution but is used in calculating risk set weights, estimates from the model based on these weights may not reflect the correct likelihood structure and therefore may have suboptimal performance.Conclusions: The estimation of the censoring distribution can affect the accuracy and conclusions of a competing risks analysis, so it is important that this issue is considered carefully when analysing time-to-event data in the presence of competing risks. [ABSTRACT FROM AUTHOR]

Background: Multi-state models are complex stochastic models which focus on pathways defined by the temporal and sequential occurrence of numerous events of interest. In particular, the so-called illness-death models are especially useful for studying probabilities associated to diseases whose occurrence competes with other possible diseases, health conditions or death. They can be seen as a generalization of the competing risks models, which are widely used to estimate disease-incidences among populations with a high risk of death, such as elderly or cancer patients. The main advantage of the aforementioned illness-death models is that they allow the treatment of scenarios with non-terminal competing events that may occur sequentially, which competing risks models fail to do. Methods: We propose an illness-death model using Cox proportional hazards models with Weibull baseline hazard functions, and applied the model to a study of recurrent hip fracture. Data came from the PREV2FO cohort and included 34491 patients aged 65 years and older who were discharged alive after a hospitalization due to an osteoporotic hip fracture between 2008-2015. We used a Bayesian approach to approximate the posterior distribution of each parameter of the model, and thus cumulative incidences and transition probabilities. We also compared these results with a competing risks specification. Results: Posterior transition probabilities showed higher probabilities of death for men and increasing with age. Women were more likely to refracture as well as less likely to die after it. Free-event time was shown to reduce the probability of death. Estimations from the illness-death and the competing risks models were identical for those common transitions although the illness-death model provided additional information from the transition from refracture to death. Conclusions: We illustrated how multi-state models, in particular illness-death models, may be especially useful when dealing with survival scenarios which include multiple events, with competing diseases or when death is an unavoidable event to consider. Illness-death models via transition probabilities provide additional information of transitions from non-terminal health conditions to absorbing states such as death, what implies a deeper understanding of the real-world problem involved compared to competing risks models. [ABSTRACT FROM AUTHOR]

Abstract Background Ensuring fair comparisons of cancer survival statistics across population groups requires careful consideration of differential competing mortality due to other causes, and adjusting for imbalances over groups in other prognostic covariates (e.g. age). This has typically been achieved using comparisons of age-standardised net survival, with age standardisation addressing covariate imbalance, and the net estimates removing differences in competing mortality from other causes. However, these estimates lack ease of interpretability. In this paper, we motivate an alternative non-parametric approach that uses a common rate of other cause mortality across groups to give reference-adjusted estimates of the all-cause and cause-specific crude probability of death in contrast to solely reporting net survival estimates. Methods We develop the methodology for a non-parametric equivalent of standardised and reference adjusted crude probabilities of death, building on the estimation of non-parametric crude probabilities of death. We illustrate the approach using regional comparisons of survival following a diagnosis of rectal cancer for men in England. We standardise to the covariate distribution and other cause mortality of England as a whole to offer comparability, but with close approximation to the observed all-cause region-specific mortality. Results The approach gives comparable estimates to observed crude probabilities of death, but allows direct comparison across population groups with different covariate profiles and competing mortality patterns. In our illustrative example, we show that regional variations in survival following a diagnosis of rectal cancer persist even after accounting for the variation in deprivation, age at diagnosis and other cause mortality. Conclusions The methodological approach of using standardised and reference adjusted metrics offers an appealing approach for future cancer survival comparison studies and routinely published cancer statistics. Our non-parametric estimation approach through the use of weighting offers the ability to estimate comparable survival estimates without the need for statistical modelling.

Background: Competing risks methodology allows for an event-specific analysis of the single components of composite time-to-event endpoints. A key feature of competing risks is that there are as many hazards as there are competing risks. This is not always well accounted for in the applied literature. Methods: We advocate a simulation point of view for understanding competing risks. The hazards are envisaged as momentary event forces. They jointly determine the event time. Their relative magnitude determines the event type. 'Empirical simulations' using data from a recent study on cardiovascular events in diabetes patients illustrate subsequent interpretation. The method avoids concerns on identifiability and plausibility known from the latent failure time approach. Results: The 'empirical simulations' served as a proof of concept. Additionally manipulating baseline hazards and treatment effects illustrated both scenarios that require greater care for interpretation and how the simulation point of view aids the interpretation. The simulation algorithm applied to real data also provides for a general tool for study planning. Conclusions: There are as many hazards as there are competing risks. All of them should be analysed. This includes estimation of baseline hazards. Study planning must equally account for these aspects. [ABSTRACT FROM AUTHOR]

Abstract Background Under competing risks, the commonly used sub-distribution hazard ratio (SHR) is not easy to interpret clinically and is valid only under the proportional sub-distribution hazard (SDH) assumption. This paper introduces an alternative statistical measure: the restricted mean time lost (RMTL). Methods First, the definition and estimation methods of the measures are introduced. Second, based on the differences in RMTLs, a basic difference test (Diff) and a supremum difference test (sDiff) are constructed. Then, the corresponding sample size estimation method is proposed. The statistical properties of the methods and the estimated sample size are evaluated using Monte Carlo simulations, and these methods are also applied to two real examples. Results The simulation results show that sDiff performs well and has relatively high test efficiency in most situations. Regarding sample size calculation, sDiff exhibits good performance in various situations. The methods are illustrated using two examples. Conclusions RMTL can meaningfully summarize treatment effects for clinical decision making, which can then be reported with the SDH ratio for competing risks data. The proposed sDiff test and the two calculated sample size formulas have wide applicability and can be considered in real data analysis and trial design.

Abstract Background Patients infected with the Human Immunodeficiency Virus (HIV) are susceptible to many diseases. In these patients, the occurrence of one disease alters the chance of contracting another. Under such circumstances, methods for competing risks are required. Recently, competing risks analyses in the scope of flexible parametric models have risen to address this requirement. These lesser-known analyses have considerable advantages over conventional methods. Methods Using data from Multi Centre AIDS Cohort Study (MACS), this paper reviews and applies methods of competing risks flexible parametric models to analyze the risk of the first disease (AIDS or non-AIDS) among HIV-infected patients. We compared two alternative subdistribution hazard flexible parametric models (SDHFPM1 and SDHFPM2) with the Fine & Gray model. To make a complete inference, we performed cause-specific hazard flexible parametric models for each event separately as well. Results Both SDHFPM1 and SDHFPM2 provided consistent results regarding the magnitude of coefficients and risk estimations compared with estimations obtained from the Fine & Gray model, However, competing risks flexible parametric models provided more efficient and smoother estimations for the baseline risks of the first disease. We found that age at HIV diagnosis indirectly affected the risk of AIDS as the first event by increasing the number of patients who experience a non-AIDS disease prior to AIDS among > 40 years. Other significant covariates had direct effects on the risks of AIDS and non-AIDS. Discussion The choice of an appropriate model depends on the research goals and computational challenges. The SDHFPM1 models each event separately and requires calculating censoring weights which is time-consuming. In contrast, SDHFPM2 models all events simultaneously and is more appropriate for large datasets, however, when the focus is on one particular event SDHFPM1 is more preferable.

Background: Royston-Parmar flexible parametric survival models (FPMs) can be fitted on either the cause-specific hazards or cumulative incidence scale in the presence of competing risks. An advantage of modelling within this framework for competing risks data is the ease at which alternative predictions to the (cause-specific or subdistribution) hazard ratio can be obtained. Restricted mean survival time (RMST), or restricted mean failure time (RMFT) on the mortality scale, is one such measure. This has an attractive interpretation, especially when the proportionality assumption is violated. Compared to similar measures, fewer assumptions are required and it does not require extrapolation. Furthermore, one can easily obtain the expected number of life-years lost, or gained, due to a particular cause of death, which is a further useful prognostic measure as introduced by Andersen.Methods: In the presence of competing risks, prediction of RMFT and the expected life-years lost due to a cause of death are presented using Royston-Parmar FPMs. These can be predicted for a specific covariate pattern to facilitate interpretation in observational studies at the individual level, or at the population-level using standardisation to obtain marginal measures. Predictions are illustrated using English colorectal data and are obtained using the Stata post-estimation command, standsurv.Results: Reporting such measures facilitate interpretation of a competing risks analysis, particularly when the proportional hazards assumption is not appropriate. Standardisation provides a useful way to obtain marginal estimates to make absolute comparisons between two covariate groups. Predictions can be made at various time-points and presented visually for each cause of death to better understand the overall impact of different covariate groups.Conclusions: We describe estimation of RMFT, and expected life-years lost partitioned by each competing cause of death after fitting a single FPM on either the log-cumulative subdistribution, or cause-specific hazards scale. These can be used to facilitate interpretation of a competing risks analysis when the proportionality assumption is in doubt. [ABSTRACT FROM AUTHOR]

Background: Time-to-event data that is subject to interval censoring is common in the practice of medical research and versatile statistical methods for estimating associations in such settings have been limited. For right censored data, non-parametric pseudo-observations have been proposed as a basis for regression modeling with the possibility to use different association measures. In this article, we propose a method for calculating pseudo-observations for interval censored data.Methods: We develop an extension of a recently developed set of parametric pseudo-observations based on a spline-based flexible parametric estimator. The inherent competing risk issue with an interval censored event of interest necessitates the use of an illness-death model, and we formulate our method within this framework. To evaluate the empirical properties of the proposed method, we perform a simulation study and calculate pseudo-observations based on our method as well as alternative approaches. We also present an analysis of a real dataset on patients with implantable cardioverter-defibrillators who are monitored for the occurrence of a particular type of device failures by routine follow-up examinations. In this dataset, we have information on exact event times as well as the interval censored data, so we can compare analyses of pseudo-observations based on the interval censored data to those obtained using the non-parametric pseudo-observations for right censored data.Results: Our simulations show that the proposed method for calculating pseudo-observations provides unbiased estimates of the cumulative incidence function as well as associations with exposure variables with appropriate coverage probabilities. The analysis of the real dataset also suggests that our method provides estimates which are in agreement with estimates obtained from the right censored data.Conclusions: The proposed method for calculating pseudo-observations based on the flexible parametric approach provides a versatile solution to the specific challenges that arise with interval censored data. This solution allows regression modeling using a range of different association measures. [ABSTRACT FROM AUTHOR]

Abstract Background To illustrate the 10-year risks of urinary adverse events (UAEs) among men diagnosed with prostate cancer and treated with different types of therapy, accounting for the competing risk of death. Methods Prostate cancer is the second most common malignancy among adult males in the United States. Few studies have reported the long-term post-treatment risk of UAEs and those that have, have not appropriately accounted for competing deaths. This paper conducts an inverse probability of treatment (IPT) weighted competing risks analysis to estimate the effects of different prostate cancer treatments on the risk of UAE, using a matched-cohort of prostate cancer/non-cancer control patients from the Surveillance, Epidemiology and End Results (SEER) Medicare database. Results Study dataset included men age 66 years or older that are 83% white and had a median follow-up time of 4.14 years. Patients that underwent combination radical prostatectomy and external beam radiotherapy experienced the highest risk of UAE (IPT-weighted competing risks: HR 3.65 with 95% CI (3.28, 4.07); 10-yr. cumulative incidence = 36.5%). Conclusions Findings suggest that IPT-weighted competing risks analysis provides an accurate estimator of the cumulative incidence of UAE taking into account the competing deaths as well as measured confounding bias.

Background: Antimalarial efficacy studies in patients with uncomplicated Plasmodium falciparum are confounded by a new infection (a competing risk event) since this event can potentially preclude a recrudescent event (primary endpoint of interest). The current WHO guidelines recommend censoring competing risk events when deriving antimalarial efficacy. We investigated the impact of considering a new infection as a competing risk event on the estimation of antimalarial efficacy in single-armed and comparative drug trials using two simulation studies.Methods: The first simulation study explored differences in the estimates of treatment failure for areas of varying transmission intensities using the complement of the Kaplan-Meier (K-M) estimate and the Cumulative Incidence Function (CIF). The second simulation study extended this to a comparative drug efficacy trial for comparing the K-M curves using the log-rank test, and Gray's k-sample test for comparing the equality of CIFs.Results: The complement of the K-M approach produced larger estimates of cumulative treatment failure compared to the CIF method; the magnitude of which was correlated with the observed proportion of new infection and recrudescence. When the drug efficacy was 90%, the absolute overestimation in failure was 0.3% in areas of low transmission rising to 3.1% in the high transmission settings. In a scenario which is most likely to be observed in a comparative trial of antimalarials, where a new drug regimen is associated with an increased (or decreased) rate of recrudescences and new infections compared to an existing drug, the log-rank test was found to be more powerful to detect treatment differences compared to the Gray's k-sample test.Conclusions: The CIF approach should be considered for deriving estimates of antimalarial efficacy, in high transmission areas or for failing drugs. For comparative studies of antimalarial treatments, researchers need to select the statistical test that is best suited to whether the rate or cumulative risk of recrudescence is the outcome of interest, and consider the potential differing prophylactic periods of the antimalarials being compared. [ABSTRACT FROM AUTHOR]

Background: In many studies, some information might not be available for the whole cohort, some covariates, or even the outcome, might be ascertained in selected subsamples. These studies are part of a broad category termed two-phase studies. Common examples include the nested case-control and the case-cohort designs. For two-phase studies, appropriate weighted survival estimates have been derived; however, no estimator of cumulative incidence accounting for competing events has been proposed. This is relevant in the presence of multiple types of events, where estimation of event type specific quantities are needed for evaluating outcome.Methods: We develop a non parametric estimator of the cumulative incidence function of events accounting for possible competing events. It handles a general sampling design by weights derived from the sampling probabilities. The variance is derived from the influence function of the subdistribution hazard.Results: The proposed method shows good performance in simulations. It is applied to estimate the crude incidence of relapse in childhood acute lymphoblastic leukemia in groups defined by a genotype not available for everyone in a cohort of nearly 2000 patients, where death due to toxicity acted as a competing event. In a second example the aim was to estimate engagement in care of a cohort of HIV patients in resource limited setting, where for some patients the outcome itself was missing due to lost to follow-up. A sampling based approach was used to identify outcome in a subsample of lost patients and to obtain a valid estimate of connection to care.Conclusions: A valid estimator for cumulative incidence of events accounting for competing risks under a general sampling design from an infinite target population is derived. [ABSTRACT FROM AUTHOR]

Background: Subjects with breast cancer enrolled in trials may experience multiple events such as local recurrence, distant recurrence or death. These events are not independent; the occurrence of one may increase the risk of another, or prevent another from occurring. The most commonly used Cox proportional hazards (Cox-PH) model ignores the relationships between events, resulting in a potential impact on the treatment effect and conclusions. The use of statistical methods to analyze multiple time-to-event events has mainly been focused on superiority trials. However, their application to non-inferiority trials is limited. We evaluate four statistical methods for multiple time-to-event endpoints in the context of a non-inferiority trial. Methods: Three methods for analyzing multiple events data, namely, i) the competing risks (CR) model, ii) the marginal model, and iii) the frailty model were compared with the Cox-PH model using data from a previouslyreported non-inferiority trial comparing hypofractionated radiotherapy with conventional radiotherapy for the prevention of local recurrence in patients with early stage breast cancer who had undergone breast conserving surgery. These methods were also compared using two simulated examples, scenario A where the hazards for distant recurrence and death were higher in the control group, and scenario B. where the hazards of distant recurrence and death were higher in the experimental group. Both scenarios were designed to have a non-inferiority margin of 1.50. Results: In the breast cancer trial, the methods produced primary outcome results similar to those using the Cox-PH model: namely, a local recurrence hazard ratio (HR) of 0.95 and a 95% confidence interval (CI) of 0.62 to 1.46. In Scenario A, non-inferiority was observed with the Cox-PH model (HR = 1.04; CI of 0.80 to 1.35), but not with the CR model (HR = 1.37; CI of 1.06 to 1.79), and the average marginal and frailty model showed a positive effect of the experimental treatment. The results in Scenario A contrasted with Scenario B with non-inferiority being observed with the CR model (HR = 1.10; CI of 0.87 to 1.39), but not with the Cox-PH model (HR = 1.46; CI of 1.15 to 1.85), and the marginal and frailty model showed a negative effect of the experimental treatment. Conclusion: When subjects are at risk for multiple events in non-inferiority trials, researchers need to consider using the CR, marginal and frailty models in addition to the Cox-PH model in order to provide additional information in describing the disease process and to assess the robustness of the results. In the presence of competing risks, the Cox-PH model is appropriate for investigating the biologic effect of treatment, whereas the CR models yields the actual effect of treatment in the study. [ABSTRACT FROM AUTHOR]

Background: Relative survival is commonly used for studying survival of cancer patients as it captures both the direct and indirect contribution of a cancer diagnosis on mortality by comparing the observed survival of the patients to the expected survival in a comparable cancer-free population. However, existing methods do not allow estimation of the impact of isolated conditions (e.g., excess cardiovascular mortality) on the total excess mortality. For this purpose we extend flexible parametric survival models for relative survival, which use restricted cubic splines for the baseline cumulative excess hazard and for any time-dependent effects. Methods: In the extended model we partition the excess mortality associated with a diagnosis of cancer through estimating a separate baseline excess hazard function for the outcomes under investigation. This is done by incorporating mutually exclusive background mortality rates, stratified by the underlying causes of death reported in the Swedish population, and by introducing cause of death as a time-dependent effect in the extended model. This approach thereby enables modeling of temporal trends in e.g., excess cardiovascular mortality and remaining cancer excess mortality simultaneously. Furthermore, we illustrate how the results from the proposed model can be used to derive crude probabilities of death due to the component parts, i.e., probabilities estimated in the presence of competing causes of death. Results: The method is illustrated with examples where the total excess mortality experienced by patients diagnosed with breast cancer is partitioned into excess cardiovascular mortality and remaining cancer excess mortality. Conclusions: The proposed method can be used to simultaneously study disease patterns and temporal trends for various causes of cancer-consequent deaths. Such information should be of interest for patients and clinicians as one way of improving prognosis after cancer is through adapting treatment strategies and follow-up of patients towards reducing the excess mortality caused by side effects of the treatment. [ABSTRACT FROM AUTHOR]

Background: In medical research, one common competing risks situation is the study of different types of events, such as disease recurrence and death. We focused on that situation but considered death under two aspects: "expected death" and "excess death", the latter could be directly or indirectly associated with the disease. Methods: The excess hazard method allows estimating an excess mortality hazard using the population (expected) mortality hazard. We propose models combining the competing risks approach and the excess hazard method. These models are based on a joint modelling of each event-specific hazard, including the event-free excess death hazard. The proposed models are parsimonious, allow time-dependent hazard ratios, and facilitate comparisons between event-specific hazards and between covariate effects on different events. In a simulation study, we assessed the performance of the estimators and showed their good properties with different drop-out censoring rates and different sample sizes. Results: We analyzed a population-based dataset on French colon cancer patients who have undergone curative surgery. Considering three competing events (local recurrence, distant metastasis, and death), we showed that the recurrence-free excess mortality hazard reached zero six months after treatment. Covariates sex, age, and cancer stage had the same effects on local recurrence and distant metastasis but a different effect on excess mortality. Conclusions: The proposed models consider the excess mortality within the framework of competing risks. Moreover, the joint estimation of the parameters allow (i) direct comparisons between covariate effects, and (ii) fitting models with common parameters to obtain more parsimonious models and more efficient parameter estimators. [ABSTRACT FROM AUTHOR]

Background: Restricted mean survival time (RMST) is an underutilized estimand in time-to-event analyses. Herein, we highlight its strengths by comparing time to (1) all-cause mortality and (2) initiation of antiretroviral therapy (ART) for HIV-infected persons who inject drugs (PWID) and persons who do not inject drugs.Methods: RMST to death was determined by integrating the Kaplan-Meier survival curve to 5 years of follow-up. To account for the competing risks of death and loss-to-clinic when estimating time to ART, we calculated RMST to ART initiation by estimating the area between the survival curve for ART initiation and the cumulative incidence curve for death or loss-to-clinic. We standardized all curves using inverse probability of exposure weights.Results: We followed 3044 HIV-positive, ART-naive persons from enrollment into the Johns Hopkins HIV Clinical Cohort from 1996 to 2014. PWID had a - 0.19 year (95% confidence interval (CI): - 0.29, - 0.10) difference in survival over 5 years of follow-up compared to persons who did not inject drugs. There was no difference between the two groups in time not on ART while alive and in clinic (RMST difference = 0.08, 95% CI: -0.10, 0.36).Conclusions: PWID have similar expected time to ART initiation after properly accounting for their greater risk of death and loss-to-clinic. [ABSTRACT FROM AUTHOR]